Image encryption method based on improved class boosting scheme

ABSTRACT

The present invention discloses an image encryption method based on an improved class boosting scheme, which comprises the following steps: acquiring parameters of a hyperchaotic system according to plaintext image information; generating weights required by class perceptron networks through the plain text image information; bringing the parameters into the hyperchaotic system to obtain chaotic sequences, and shuffling the chaotic sequences by a shuffling algorithm; pre-processing the chaotic sequences after shuffling to obtain a sequence required by encryption: and bringing a plaintext image and the sequence into an improved class boosting scheme to obtain a ciphertext image, wherein the improved class boosting scheme is realized based on the class perception networks. The method solves the problems that update and prediction functions in an original boosting network are too simple and easy to predict or the like, so as to obtain the ciphertext image with higher information entropy.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the priority of Chinese patentapplication filed in China Patent Office on Sep. 18, 2021, with theapplication No. 202111111709.5 and entitled “an image encryption methodbased on improved class boosting scheme”, the entire contents of whichare incorporated in the present application by reference.

TECHNICAL FIELD

The present invention relates to the technical field of imageencryption, in particular to an image encryption method based on animproved class boosting scheme.

BACKGROUND

With the rapid development of Internet and multimedia technology, it ismore and more convenient for people to get information on the Internet.Because images carry private and sensitive information, the security ofimage information has drawn more attention. The image encryptiontechnology is one of the most effective means to ensure the security ofimage information. Zhang Yong proposed a unified image encryption systembased on a class boosting scheme, which uses class boostingtransformation to diffuse image information, thereby realizing imageencryption. Although the system has a fast encryption and decryptionspeed and a good encryption effect, it has the disadvantages that updateand prediction functions are too simple: and it is easy for a decodingperson to find out a linear relationship, so as to solve it. Therefore,it is positive work to study more complex update and predictionfunctions to improve the security and reliability of image encryption.

SUMMARY

Aiming at the problem that update and prediction functions in a classboosting scheme in the prior art are too simple, the present inventionprovides an image encryption method based on the improved class boostingscheme, which combines class perception networks with a class boostingscheme to achieve a better encryption effect.

To achieve the above purpose, the present invention provides an imageencryption method based on an improved class boosting scheme, whichcomprises:

-   -   acquiring parameters of a hyperchaotic system according to        plaintext image information;    -   generating weights required by class perceptron networks through        the plaintext image information;    -   bringing the parameters into the hyperchaotic system to obtain        chaotic sequences, and shuffling the chaotic sequences by a        shuffling algorithm;    -   pre-processing the chaotic sequences after shuffling to obtain a        sequence required by encryption; and    -   bringing a plaintext image and the sequence into an improved        class boosting scheme to obtain a ciphertext image, wherein the        improved class boosting scheme is realized based on the class        perception networks.

Further, wherein acquiring the parameters of the hyperchaotic systemaccording to the plaintext image information specifically comprises;generating a hash value K of the plaintext image by a SHA512 function,converting the hash value K into a binary number, and then generating128 groups of decimal numbers H=h₁, h₂, h₃, . . . , h₁₂₈ by 4 hits ineach group, and then obtaining a hyperchaotic initial value by thedecimal number group H, which is specifically:

$x_{0} = {{mod}\left( {{{mean}\left( {\sum\limits_{i = 1}^{32}h_{i}} \right)},1} \right)}$$x_{1} = {{mod}\left( {{{mean}\left( {\sum\limits_{i = 33}^{64}h_{i}} \right)},1} \right)}$$x_{2} = {{mod}\left( {{{mean}\left( {\sum\limits_{i = 65}^{96}h_{i}} \right)},1} \right)}$$x_{3} = {{{mod}\left( {{{mean}\left( {\sum\limits_{i = 97}^{128}h_{i}} \right)},1} \right)}.}$

Further, wherein generating the weights required by the class perceptronnetworks through the plaintext image information specifically comprises:generating initial weights of two class perceptron networks by thedecimal number group H=h₁, h₂, h₃, . . . , h₁₂₈, wherein weights of theclass perceptron network PLN-1 are respectively:φ₁₁=mod(sum(h ₁ h ₂ . . . h ₃₂)×10¹⁰,9)φ₁₂=mod(sum(h ₃₃ h ₃₄ . . . h ₆₄)×10¹⁰,9)φ₂₁=mod(sum(h ₆₅ h ₆₆ . . . h ₉₆)×10¹⁰,9)φ₂₂=mod(sum(h ₉₇ h ₉₈ . . . h ₁₂₈)×10¹⁰,9);and

weights φ′₁₁, φ′₁₂, φ′₂₁, φ′₂₂ of the perceptron network PLN-2 arerespectively:φ′₁₁=floor(mean(h ₁ h ₂ . . . h ₃₂))φ′₁₂=floor(mean(h ₃₃ h ₃₄ . . . h ₆₄))φ′₂₁=floor(mean(h ₆₅ h ₆₆ . . . h ₉₆))φ′₂₂=floor(mean(h ₉₇ h ₉₈ . . . h ₁₂₈))

Further, wherein bringing the parameters into the hyperchaotic system toobtain the chaotic sequences, and shuffling the chaotic sequences by theshuffling algorithm specifically comprise:

bringing the parameters into the hyperchaotic system to generate foursequences a₁, a₂, a₃ and a₄ with the length of M×N+300, discarding thefirst 300 elements of each sequence, and processing the remainingsequences as follows, so as to obtain sequences within a scope of normalplaintext pixel values, namely (i=1, 2, 3, . . . , n), whereinb ₁(i)=mod(abs(floor(a ₁(i)×10¹⁰)),256)b ₂(i)=mod(abs(floor(a ₂(i)×10¹⁰)),256)b ₃(i)=mod(abs(floor(a ₃(i)×10¹⁰)),256)b ₄(i)=mod(abs(floor(a ₄(i)×10¹⁰)),256)

generating a random value array (i=1, 2, 3, . . . , n) used for aKnuth-Durstenfeld shuffling algorithm, wherein NUM is the total sequencelength; andaa ₁(i)=mod(abs(floor(a ₁(i)×10¹⁰)),NUM−i+1)+1aa ₂(i)=mod(abs(floor(a ₂(i)×10¹⁰)),NUM−i+1)+1aa ₃(i)=mod(abs(floor(a ₃(i)×10¹⁰)),NUM−i+1)+1aa ₄(i)=mod(abs(floor(a ₄(i)×10¹⁰)),NUM−i+1)+1

shuffling the generated sequences by the shuffling algorithm with thegenerated random value array.

Further, wherein pre-processing the chaotic sequences after shuffling toobtain the sequence required by encryption specifically comprises: altershuffling the obtained sequences b₁, b₂, b₃ and b₄ with the shufflingalgorithm, taking the first numbers in b₁, b₂, b₃ and b₄ arrays as agroup to sere as the first four numbers in the sequence {a_(i)}; takingthe second numbers in the b₁, b₂, b₃ and b₄ arrays as a group andinserting the numbers into the sequence {a_(i)}, repeating the abovesteps until there are M×N/2 numbers in the sequence {a_(i)}, generatingthe required sequence {a_(i)}, where i=1, 2, 3, . . . , M×N/2, anddirectly using the sequence for image encryption, wherein M is thenumber of rows of the plaintext image; and N is the number of columns ofthe plaintext image.

Further, wherein the improved class boosting scheme comprises a forwardtransformation module, an overturning transformation module and aninverse transformation module; and operations in the three modules areall based on a GF(2⁸) domain.

Further, wherein in the forward transformation module, the plaintextimage is first converted into a one-dimensional sequence {x_(i)}, wherei=1, 2, 3, . . . , M×N; and then the sequence {x_(i)} is divided intotwo subsequences {e_(j)} and {o_(j)}, where e_(j)=x_(2j−1);o_(j)=x_(2j); and j=1, 2, 3, . . . L;

a sequence {p_(j)} is obtained from the subsequence {e_(j)} and thesequence {a_(i)} as follows:

p_(j)=e_(j)+a_(i); where j=1, 2, 3, . . . , L;

after the sequence {p_(j)} as updated by the class perceptron networkPLN-1, the sequence is combined with the subsequence {o_(j)} to obtain asequence {d_(j)} as follows:

d_(j)=d_(j−1)+o_(j)+PLN-1(p_(j),p_(j+1)), where j=1, 2, 3, . . . , L;

d₀=0; and P₀=0; and

after the sequence {s_(j)} is updated by the class perceptron networkPLN-2, the sequence is combined with the sequence {p_(j)} to obtain asequence {s_(j)} as follows:

s_(j)=p_(j)+p_(j−1)+PLN-2(d_(j−1),d_(j)), where j=1, 2, 3, . . . , L;and

d₀=0; and P₀=0; and

the obtained sequences {s_(j)} and {d_(j)} are combined into a newsequence {r_(i)}, where i=1, 2, 3, . . . , M×N; R_(2j−1)=S_(j);R_(2J)=D_(j); and j=1, 2, 3, . . . , L.

Further, wherein in the forward transformation module, the sequence{r_(i)}, where i=1, 2, 3, . . . , M×N, is flipped left and right in theoverturning module to obtain a new sequence {r′_(i)}, where i=1, 2, 3, .. . , M×N.

Further, wherein in the forward transformation module, the sequence{r′_(i)} is divided into two different sequences {s′_(j)} and {d′_(j)}according to an odd even index in the inverse transformation module,where s′_(j)=r′_(2j−1); d′_(j)=r′_(2j); and j=1, 2, 3, . . . L;

after the sequence {d′_(j)} is updated by the class perceptron networkPLN-2, the sequence is combined with the sequence {s′_(j)} to obtain asequence {S′_(j)} as follows:

S′_(j)=s′j−S′_(j−1)−PLN-2(d′_(j−1),d′_(j)), where j=1, 2, 3, . . . L;

d′₀=0; and S′₀=0;

after {S′_(j)} is updated by the class perceptron network PLN-1, thesequence is combined with the sequence {d′_(j)} to obtain a sequence{o′_(j)} as follows:

o′_(j)=d′_(j)−d′_(j−1)−PLN-1(S′_(j),S′_(j+1)), where j=1, 2, 3, . . . L;

d′₀=0; and S′_(L+1)=0;

a sequence {e′_(j)} obtained from the sequence {S′_(j)} and the sequence{a_(i)} is:

e′_(j)=S′_(j)-a_(i), where j=1, 2, 3, . . . L;

{e′_(j)} and {o′_(j)} are combined into a new sequence {y_(i)}, wherei=1, 2, 3, . . . , M×N; Y_(2j−1)=e′_(j); Y_(2j)=o′_(j); and j=1, 2, 3, .. . L; and

finally, the obtained sequence is converted into a matrix with the sizeof M×N, that is, an encrypted image is obtained.

According to specific embodiments provided by the present invention, thepresent invention discloses the following technical effects:

-   -   1. Compared with a traditional permutation diffusion structure,        the scheme has a faster encryption and decryption speed and has        higher information entropy and a better encryption effect when        only one round of encryption is needed;    -   2. Different from an original class boosting scheme, the present        invention makes an original linear function become a complex        structure combining linear and nonlinear functions by taking        class perceptron networks as prediction and update functions of        the class boosting scheme. Moreover, parameters of the class        perceptron networks are related to a plaintext. Meanwhile, there        is a function of self-updating, which can make each operation        different, thereby increasing randomness and unpredictability of        image encryption, and being of great significance to security of        image encryption; and    -   3. Parameters required by chaotic sequences and the class        perception networks are related to a plaintext image, so that        the parameters generated by different images are different,        thereby greatly improving randomness and security of encryption.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic structural diagram of a class perceptron network;

FIG. 2 is a schematic diagram of an improved class boosting scheme:

FIG. 3 is a comparison diagram of encryption and decryption using themethod of the present invention;

FIG. 4 is an analysis histogram of an embodiment using the method of thepresent invention; and

FIG. 5 is a comparison diagram of pixel correlations between a Lenaoriginal image and an encrypted image.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention comprises the following steps: firstly, generatinga HASH value of a plait/text image by a HAS512 function, generatingparameters required by a hyperchaotic system and weights required byclass perceptron networks by the HASH value; secondly, shufflinggenerated chaotic sequences by a shuffling algorithm; and finally,bringing an obtained random sequence and the plaintext image into animproved class boosting scheme to obtain a final ciphertext image. Inthe process of decryption, the plaintext image can be recovered withoutany loss only by bringing the ciphertext image and a key into theimproved class boosting scheme.

A chaotic system used in the present invention is a hyperchaotic system.

$\left\{ \begin{matrix}{\frac{{dx}_{1}}{dt} = {m \times \left( {x_{2} - x_{1}} \right)}} \\{\frac{{dx}_{2}}{dt} = {{{- x_{1}} \times x_{3}} + {q \times x_{1}} + {p \times}}} \\{\frac{{dx}_{3}}{dt} = {{x_{1} \times x_{2}} - {n \times x_{3}}}} \\{\frac{{dx}_{4}}{dt} = {{x_{2} \times x_{3}} + {r \times x_{4}}}}\end{matrix} \right.$

where in

$\frac{{dx}_{i}}{dt},$i=1, 2, 3, 4 is a derivative of time t; and m, n, p, q and r areparameters of the chaotic system. When m=35, n=3, p=12, q=7 and r=0.58,the system is called a hyperchaotic system.

A Knuth-Durstenfeld shuffling algorithm used in the present inventioncomprises the following specific steps:

Step 1: Storing an array with the length of n in an array arr[ ].

Step 2: Generating a random number [1,n], taking the generated randomnumber as an array subscript and outputting as x.

Step 3: Swapping the output x with the last element in the array arr[ ].

Step 4: Generating a random number [1,n−1], taking the generated randomnumber as an array subscript, and outputting as x′.

Step 5: Swapping the output x′ with the penultimate element in the arrayarr[ ].

The above steps are repeated until all n numbers are processed.

As shown in FIGS. 1-2 , specific steps of an encryption process andweight update of class perceptron networks used in the present inventionare as follows:

Step 1: inputting signals x₁ and x₂ for linear transformation to obtainx′₁ and x′₂ of a hidden layer:x′ ₁ =x ₁×ω₁₁ +x ₂×ω₂₁x′ ₂ =x ₁×ω₁₂ +x ₂×ω₂₂

Step 2: replacing a weight from the hidden layer to an output layer by afunction f(x), wherein an or result of the output layer is as follows.y′ ₁ =f(x′ ₁)y′ ₂ =f(x′ ₂)

Where: f(x)=mod(x, 16).

Step 3: calculating an output signal y through S-box.y=S-box(y′ ₁ ,y′ ₂).

Step 4; automatically updating height functions.ω₁₁=ω₁₁+mod(x ₁,2)ω₁₂=ω₁₂+mod(x ₂,2)ω₂₁=ω₂₁+mod(x ₁,2)ω₂₂=ω₂₂+mod(x ₂,2)

Initial weights of class perceptron networks are generated by the HASHvalue.

Embodiment 1

An embodiment of the present invention is implemented based on thetechnical solution of the present invention. Detailed implementationsand specific operation processes are given, but the protection scope ofthe present invention is not limited to the following embodiment. In thepresent embodiment, lena256×256 image is used; and a HASH value isgenerated by a HASH function. After processing, original parameters of ahyperchaotic system are x₁=0.37; x₂=0.5313; x₃=0.1875; and x₄=0.2500.Parameters of class perceptron networks are respectively as follows. InPLN-1, W₁₁=7; W₁₂=7; W₂₁=7; and W₂₂=6. In PLN-2, w₁₁=2; w₁₂=7; w₂₁=5;and w₂₂=2.

Step 1: bringing the original parameters into the hyperchaotic system togenerate four sequences a₁, a₂, a₃, and a₄ with the length of M×N+300,discarding the first 300 elements of each sequence, and processing theremaining sequences as follows.b ₁(i)=mod(abs(floor(a ₁(i)×10¹⁰)),256)b ₂(i)=mod(abs(floor(a ₂(i)×10¹⁰)),256)b ₃(i)=mod(abs(floor(a ₃(i)×10¹⁰)),256)b ₄(i)=mod(abs(floor(a ₄(i)×10¹⁰)),256)

Step 2: using the four sequences a₁, a₂, a₃ and a₄ to generate randomarrays aa₁, aa₂, aa₃ and aa₄ used for a shuffling algorithm, andshuffling b₁, b₂, b₃ and b₄ by the shuffling algorithm. The algorithm togenerate aa₁, aa₂, aa₃ and aa₄ are as follows.aa ₁(i)=mod(abs(floor(a ₁(i)×10¹⁰)),NUM−i+1)+1aa ₂(i)=mod(abs(floor(a ₂(i)×10¹⁰)),NUM−i+1)+1aa ₃(i)=mod(abs(floor(a ₃(i)×10¹⁰)),NUM−i+1)+1aa ₄(i)=mod(abs(floor(a ₄(i)×10¹⁰)),NUM−i+1)+1

Step 3: preprocessing the obtained sequences b₁, b₂, b₃ and b₄ with theshuffling algorithm in step 2, taking the first numbers in b₁, b₂, b₃and b₄ arrays as a group to serve as the first four numbers in thesequence {a_(i)}; taking the second numbers in the b₁, b₂, b₃ and b₄arrays as a group and inserting the numbers into the sequence {a_(i)},repeating the above steps until there are M×N/2 numbers in the sequence{a_(i)}, generating the required sequence {a_(i)}, where i=1, 2, 3, . .. , M×N/2, and directly using the sequence for image encryption.

Step 4. Bringing the obtained sequence {a_(i)} together with theplaintext image into the improved class boosting scheme to generate afinal ciphertext image.

The present invention proposes an image encryption method based on animproved class boosting scheme, which greatly enhances unpredictabilityof the scheme by adding the class perceptron networks into the improvedclass boosting scheme, and can obtain a better encryption result. Thepresent invention carries out simulation on a computer based on anIntel®Core™i5-9400CPU@2.90 GHz2.90 GHz 64-bit operation system, and anx64 processor; and the programming language used is MATLAB2019b. Afterthe above encryption method is applied to image processing, FIGS. 3-5show that the present invention has a good encryption effect.

In this paper, specific embodiments are used to explain the principleand implementations of the present invention; and the explanations ofthe above embodiments are only used to help understand the method andcore ideas of the present invention. Meanwhile, according to the idea ofthe present invention, there will be some changes in the specificimplementations and application scope for those ordinarily skilled inthe art. To sum up, the contents of the specification should not beunderstood as limitations to the present invention.

What is claimed is:
 1. An image encryption method based on an improvedclass boosting scheme, comprising: acquiring parameters of ahyperchaotic system according to plaintext image information; generatingweights required by class perceptron networks through the plaintextimage information; bringing the parameters into the hyperchaotic systemto obtain chaotic sequences, and shuffling the chaotic sequences by ashuffling algorithm; pre-processing the chaotic sequences aftershuffling to obtain a sequence required by encryption; and bringing aplaintext image and the sequence into an improved class boosting schemeto obtain a ciphertext image, wherein the improved class boosting schemeis realized based on the class perceptron networks; wherein acquiringthe parameters of the hyperchaotic system according to the plaintextimage information specifically comprises: generating a hash value K ofthe plaintext image by a SHA512 function, converting the hash value Kinto a binary number, and then generating 128 groups of decimal numbersH=h₁, h₂, h₃, . . . , h₁₂₈ by 4 bits in each group, and then obtaining ahyperchaotic initial value by the decimal number group H, which isspecifically:$x_{0} = {{mod}\left( {{{mean}\left( {\underset{i = 1}{\sum\limits^{32}}h_{i}} \right)},l} \right)}$$x_{1} = {{mod}\left( {{{mean}\left( {\underset{i = 33}{\sum\limits^{64}}h_{i}} \right)},l} \right)}$$x_{2} = {{mod}\left( {{{mean}\left( {\underset{i = 65}{\sum\limits^{96}}h_{i}} \right)},l} \right)}$$x_{3} = {{{mod}\left( {{{mean}\left( {\underset{i = 97}{\sum\limits^{128}}h_{i}} \right)},l} \right)}.}$2. The image encryption method based on the improved class boostingscheme according to claim 1, wherein generating the weights required bythe class perceptron networks through the plaintext image informationspecifically comprises: generating initial weights of two classperceptron networks by the decimal number group H=h₁, h₂, h₃, . . . ,h₁₂₈, wherein weights of the class perceptron network PLN-1 arerespectively:φ₁₁=mod(sum(h ₁ h ₂ . . . h ₃₂)×10¹⁰,9)φ₁₂=mod(sum(h ₃₃ h ₃₄ . . . h ₆₄)×10¹⁰,9)φ₂₁=mod(sum(h ₆₅ h ₆₆ . . . h ₉₆)×10¹⁰,9)φ₂₂=mod(sum(h ₉₇ h ₉₈ . . . h ₁₂₈)×10¹⁰,9);and weights φ′₁₁, φ′₁₂, φ′₂₁,φ′₂₂ of the perceptron network PLN-2 are respectively:φ′₁₁=floor(mean(h ₁ h ₂ . . . h ₃₂))φ′₁₂=floor(mean(h ₃₃ h ₃₄ . . . h ₆₄))φ′₂₁=floor(mean(h ₆₅ h ₆₆ . . . h ₉₆))φ′₂₂=floor(mean(h ₉₇ h ₉₈ . . . h ₁₂₈))
 3. The image encryption methodbased on the improved class boosting scheme according to claim 1,wherein bringing the parameters into the hyperchaotic system to obtainthe chaotic sequences, and shuffling the chaotic sequences by theshuffling algorithm specifically comprise: bringing the parameters intothe hyperchaotic system to generate four sequences a₁, a₂, a₃ and a₄with the length of M×N+300, discarding the first 300 elements of eachsequence, and processing the remaining sequences as follows, so as toobtain sequences within a scope of normal plaintext pixel values, namely(i=1, 2, 3, . . . , n), whereinb ₁(i)=mod(abs(floor(a ₁(i)×10¹⁰)),256)b ₂(i)=mod(abs(floor(a ₂(i)×10¹⁰)),256)b ₃(i)=mod(abs(floor(a ₃(i)×10¹⁰)),256)b ₄(i)=mod(abs(floor(a ₄(i)×10¹⁰)),256) generating a random value array(i=1, 2, 3, . . . , n) used for a Knuth-Durstenfeld shuffling algorithm,wherein NUM is the total sequence length; andaa ₁(i)=mod(abs(floor(a ₁(i)×10¹⁰)),NUM−i+1)+1aa ₂(i)=mod(abs(floor(a ₂(i)×10¹⁰)),NUM−i+1)+1aa ₃(i)=mod(abs(floor(a ₃(i)×10¹⁰)),NUM−i+1)+1aa ₄(i)=mod(abs(floor(a ₄(i)×10¹⁰)),NUM−i+1)+1; and shuffling thegenerated sequences by the shuffling algorithm with the generated randomvalue array.
 4. The image encryption method based on the improved classboosting scheme according to claim 1, wherein pre-processing the chaoticsequences after shuffling to obtain the sequence required by encryptionspecifically comprises: after shuffling the obtained sequences b₁, b₂,b₃ and b₄ with the shuffling algorithm, taking the first numbers in b₁,b₂, b₃ and b₄ arrays as a group to serve as the first four numbers inthe sequence {a_(i)}; taking the second numbers in the b₁, b₂, b₃ and b₄arrays as a group and inserting the numbers into the sequence {a_(i)},repeating the above steps until there are M×N/2 numbers in the sequence{a_(i)}, generating the required sequence {a_(i)}, where i=1, 2, 3, . .. , M×N/2, and directly using the sequence for image encryption, whereinM is the number of rows of the plaintext image; and N is the number ofcolumns of the plaintext image.
 5. The image encryption method based onthe improved class boosting scheme according to claim 1, wherein theimproved class boosting scheme comprises a forward transformationmodule, an overturning transformation module and an inversetransformation module; and operations in the three modules are all basedon a GF(2⁸) domain.
 6. The image encryption method based on the improvedclass boosting scheme according to claim 5, wherein in the forwardtransformation module, the plaintext image is first converted into aone-dimensional sequence {x_(i)}, where i=1, 2, 3, . . . , M×N; and thenthe sequence {x_(i)} is divided into two subsequences {e_(j)} and{o_(j)}, where e_(j)=x_(2j−1); o_(j)=x_(2j); and j=1, 2, 3, . . . , L; asequence {p_(j)} is obtained from the subsequence {e_(j)} and thesequence {a_(i)} as follows: p_(j)=e_(j)+a_(i), where j=1, 2, 3, . . . ,L; after the sequence {p_(j)} is updated by the class perceptron networkPLN-1, the sequence is combined with the subsequence {o_(j)} to obtain asequence {di} as follows: d_(j)=d_(j−i)+o_(j)+PLN-1(p_(j),p_(j+1)),where j=1, 2, 3, . . . , L; d₀=0; and p_(L+1)=0; after the sequence{d_(j)} is updated by the class perceptron network PLN-2, the sequenceis combined with the sequence {p_(j)} to obtain a sequence {s_(j)} asfollows: s_(j)=p_(j)+p_(j−i)+PLN-2(d_(j−1),d_(j)), where j=1, 2, 3, . .. , L; and d₀=0; and P₀=0; and the obtained sequences {s_(j)} and{d_(j)} are combined into a new sequence {r_(i)}, where i=1, 2, 3, . . ., M×N; R_(2j−1)=S_(j); R_(2J)=D_(j); and j=1, 2, 3, . . . , L.
 7. Theimage encryption method based on the improved boosting scheme accordingto claim 6, wherein in the forward transformation module, the sequence{r_(i)}, where i=1, 2, 3, . . . , M×N, is flipped left and right in theoverturning module to obtain a new sequence {r′_(i)}, where i=1, 2, 3, .. . , M×N.
 8. The image encryption method based on the improved boostingscheme according to claim 7, wherein in the forward transformationmodule, the sequence {r′_(i)} is divided into two different sequences{s′_(j)} and {d′_(j)} according to an odd-even index in the inversetransformation module, where s′_(j)=r′_(2j−1); d′_(j)=r′_(2j); and j=1,2, 3, . . . L; after the sequence {d′_(j)} is updated by the classperceptron network PLN-2, the sequence is combined with the sequence{s′_(j)} to obtain a sequence {S′_(j)} as follows:S′_(j)=s′_(j−1)−PLN-2(d′_(j−1),d′_(j)), where j=1, 2, 3, . . . L; d′₀=0;and S′₀=0; after {S′_(j)} is updated by the class perceptron networkPLN-1, the sequence is combined with the sequence {d′_(j)} to obtain asequence {o′_(j)} as follows:o′_(j)=d′_(j)−d′_(j−1)−PLN-1(S′_(j),S′_(j+1)), where j=1, 2, 3, . . . L;d′₀=0; and S′_(L+1)=0; a sequence {e′_(j)} obtained from the sequence{S′_(j)} and the sequence {a_(i)} is: e′_(j)=S′_(j)−a_(i), where j=1, 2,3, . . . L; {e′_(j)} and {o′_(j)} are combined into a new sequence{y_(i)}, where i=1, 2, 3, . . . , M×N; Y_(2j−1)=e′_(j); Y_(2j)=o′_(j);and j=1, 2, 3, . . . L; and finally, the obtained sequence is convertedinto a matrix with the size of M×N, that is, an encrypted image isobtained.